nbo10 said:Who said it failed?
The free electron model (as put forth by Drude, and modified by Sommerfeld and others) "failed" because for the most part, electrons aren't completely free. They interact with (i) the lattice, (ii) each other, and (iii) impurities. Drude incorporated (i) into his model in the form of a hard-sphere interaction, but completely neglected the other interactions. Sommerfeld made some corrections to this purely classical model, by ensuring that the electron gas obey Fermi statistics. This fixed some problems (like the overestimates of the electronic heat capacity), but still didn't cover for the missing interactions in the model.ziadett said:why did the free electron theory of metals fail (the free electron model)?
The free electron theory of metals is a model used to explain the behavior of electrons in metallic substances. It proposes that the valence electrons in a metal are not bound to a specific atom, but rather move freely throughout the entire metal lattice.
One of the main limitations of the free electron theory is that it fails to account for the observed resistivity of metals at low temperatures. This is known as the "resistivity plateau" and is not predicted by the theory. Additionally, the free electron theory does not explain the existence of energy bands in metals, which is a fundamental concept in modern solid state physics.
Several alternative theories have been proposed to explain the behavior of electrons in metals, including the band theory of solids, the Fermi liquid theory, and the nearly-free electron model. These theories take into account the concept of energy bands and provide a more accurate description of electron behavior in metals.
The failure of the free electron theory has led to the development of more sophisticated theories that better explain the properties of metals. It has also allowed for a deeper understanding of the electronic structure of metals and how it contributes to their physical properties. Furthermore, the failure of the free electron theory has highlighted the need for continued research and development in the field of solid state physics.
Yes, the failure of the free electron theory has practical implications in the development of new materials and technologies. By understanding the limitations of the theory, scientists are able to design and engineer materials with specific electronic properties, leading to advancements in fields such as electronics, energy storage, and materials science.